Question

Before looking it up, predict intrinsic spin (i.e., actual angular momentum) of the deuteron, \({ }_{1}^{2} \mathrm{H}\). Explain your reasoning. (Hint: Nucleons are fermions.)

Short answer

Answer: The intrinsic spin of a deuteron is 1.

Step-by-step solution

Identify the components of the deuteron

A deuteron is composed of one proton and one neutron.

Consider the spin of a proton and a neutron

Both protons and neutrons are fermions, and thus they both have half-integer spins. Specifically, a proton has a spin of \(\dfrac{1}{2}\), and a neutron also has a spin of \(\dfrac{1}{2}\).

Calculate the total spin

Since the deuteron consists of one proton and one neutron, we need to add their spins together to get the total spin. There are two possibilities: either their spins align, or they don't align.

Step 3.1: Case 1 - Aligned Spins

If the spins of the proton and neutron align, their spins will add up, and the total spin would be: \(\dfrac{1}{2}+\dfrac{1}{2}=1\)

Step 3.2: Case 2 - Opposite Spins

If the spins of the proton and neutron are opposite, their spins will subtract, and the total spin would be: \(\dfrac{1}{2} - \dfrac{1}{2} = 0\)

Determine the likely intrinsic spin of the deuteron

Considering both cases, we find that the intrinsic spin of the deuteron will be either \(1\) or \(0\). However, due to binding energy considerations and experimental observation, it turns out that the binding energy is minimized when the spins are aligned. Therefore, the deuteron has an intrinsic spin of \(1\).

Key concepts

Nuclear Physics

Nuclear physics is a branch of physics that deals with the constituents and behavior of atomic nuclei. This field seeks to understand the properties of nuclear matter under different conditions, such as the force that binds protons and neutrons together in the nucleus.

Nuclear physics is critical to understanding how elements are formed through nuclear fusion and fission processes. For instance, in the exercise, we're looking at the deuteron, the nucleus of deuterium, which serves as a simple yet fundamental system in nuclear physics to study the interactions between nucleons.

Fermions

Fermions are a class of particles named after the Italian physicist Enrico Fermi. One of the key characteristics of fermions is that they follow the Pauli exclusion principle, which states that no two identical fermions can occupy the same quantum state simultaneously.

In the context of our exercise, both protons and neutrons are fermions with half-integer spins. This means that they exhibit behaviors like antisymmetry under particle exchange, leading to their unique arrangement in an atomic nucleus and significantly influencing their interaction dynamics.

Angular Momentum

Angular momentum, in physics, is a measure of the amount of rotation an object has, taking into account its mass, shape, and speed. It’s a conserved quantity, meaning it remains constant in a closed system unless acted on by an outside torque.

The intrinsic spin of particles like protons and neutrons is a form of angular momentum. It's an intrinsic property, much like mass or charge, that doesn't depend on any motion through space. As highlighted in the exercise solution, these spins can combine in different ways to determine the total angular momentum of a system, such as the deuteron.

Nucleons

Nucleons are the building blocks of an atomic nucleus and include protons and neutrons. Protons carry a positive charge, while neutrons are neutral. Despite their charge difference, both have nearly the same mass and are held together in the nucleus by the strong nuclear force, which is much stronger than the electromagnetic force repelling the positively charged protons.

In our exercise, the deuteron consists of one proton and one neutron. The strong force between these two nucleons allows for the existence of a stable deuteron with measurable properties, such as its intrinsic spin, which is essential for understanding nuclear structure and stability.